And how would you solve this?

If you connect point G to C then we can say that the area of the whole square (Ar. \text{ACEF})= area of two right-angle triangles (\triangle CAF & \triangle CEF)

Now, to get the area of of shaded region we just need to subtract the area of \triangle DGC from \triangle CEF (These two triangle are both right-angle)

Thus, you can select a random value for side of the square and use the 45-45-90 ratio to solve it

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Thank you! Just to make sure the answer is C, correct?

Yeah!